Calculate the area of the region enclosed by the x-axis and one arch of the curve y=sin x.
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The area bounded by the curve y = sin x and x axis is the definite integral of the given function.
Since the boundary lines are not given, we'll suppose that x = -pi/2 and x = pi/2.
Int sin x dx = -cos x
We'll apply Leibniz Newton formula:
Int sin x dx = F(b) - F(a)
a = -pi/2 and b = pi/2Since the sine function is odd, we'll consider the integral as:
Int sin x dx = 2 Int sin x dx from x = 0 to x = pi/2.
2Int sin x dx = 2[-cos (pi/2) + cos 0]
2Int sin x dx = 2(0 + 1)
2Int sin x dx = 2
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